You make this kind of statement a lot. — frank

In reply to you, yes, indeed.

I'm sure you can find someone to engage you. It's not going to be me. :razz: — frank

Then why do you insist on engaging? You are, after all, on this thread, replying to my posts, and you need not be.

That's classic passive aggressive shite: "I'M NOT GOING TO TALK TO YOU, IN THE LOUDEST WAY POSSIBLE".

(I accidentally bumped the caps lock there, but decided to let it stand.)

If I am using "know" metaphorically, ironically, wryly, jokingly, humorously or sarcastically, it is not being used incorrectly. — RussellA

Sure, you can use it any way you like, but if you want to maintain a distinction between knowing and believing, then I don't think loose or ambiguous usages are a good idea.

I think the kinds of uses you refer to have no philosophical significance other than the already uncontroversial point that there are other kinds of linguistic usages apart from the strictly propositional.

Meta's posts, as always, serve only to confuse. — Banno

To put that more correctly, Meta's posts, as usual, serve to show that the subject is confused.

Sure, you can use it any way you like, but if you want to maintain a distinction between knowing and believing, then I don't think loose or ambiguous usages are a good idea. — Janus

Totally agree, exactly my point.

Exactly wrong. — Banno

True. My new understanding is:

From the SEP Rigid Designators, Kripke addresses the objection that we cannot talk about someone without first having some qualitative criterion of identity, an essence, and if we know of no such essence we cannot meaningfully talk about someone.

Kripke addresses the objection that we cannot meaningfully talk about you, with respect to another possible world, without first having some qualitative criterion of identity, some qualitatively distinguishing mark that allows us to pick you out from other objects in the world at issue, in order to assign your name to the right person, i.e., to you, as the individual that satisfies the qualitative criterion. This criterion would appeal to your essence (or be “an essence”: see Plantinga 1985, pp. 85–7; 1974, p. 98; recall, for this example, the minimal requirements of weak necessity), in the minimal respect that the criterion must be something that you and you alone have with respect to any given possible world. As an objection, the worry is that we know of no such qualitative criterion so we can not meaningfully discuss you, with respect to any merely possible world.

From Wikipedia Causal Theory of Reference, Kripke outlined a causal theory of names whereby you don't need to be able to describe what is being named, but after naming an individual in an "initial baptism" the name continues to refer through a causal chain. In fact, although the meaning of the name may change with time and use, the new meaning becomes the new "reality".

1) a name's referent is fixed by an original act of naming (also called a "dubbing" or, by Saul Kripke, an "initial baptism"), whereupon the name becomes a rigid designator of that object.
2) later uses of the name succeed in referring to the referent by being linked to that original act via a causal chain.

In lectures later published as Naming and Necessity, Kripke provided a rough outline of his causal theory of reference for names. Although he refused to explicitly endorse such a theory, he indicated that such an approach was far more promising than the then-popular descriptive theory of names introduced by Russell, according to which names are in fact disguised definite descriptions. Kripke argued that in order to use a name successfully to refer to something, you do not have to be acquainted with a uniquely identifying description of that thing. Rather, your use of the name need only be caused (in an appropriate way) by the naming of that thing.

Notice that this doesn't mean you can't have a description in mind when you talk about Paris, for instance. It just means it isn't necessary.

I didn't, but I knew about the phenomena. It's why I prefer the thermometer as a basis for theorizing heat :) -- whatever is being picked out by the measuring of thermometers is at least related to heat. And, perhaps in this way, we might say that "heat" is a rigid designator -- we're picking out the same phenomena across different instruments, at least, and seem to be trying to talk about the same phenomena even in positing different descriptions of that phenomena.

I think that's where my thoughts are coalescing at the moment -- to be able to even talk about a counter-factual, if all names were were descriptions, then by positing a different description of a named object we'd be picking out something different. Counter-factuals would actually just be us talking about different objects no matter what. That's why using "this" (though I'm picking up what you mean by "this" not being a name, now, ala Kripke -- since that's what he's speaking against, is Russel's theory of "this" counting as a name) with the lectern sunk home with me -- if descriptions are really all there are to names, then "this lectern is made of ice" is already picking out another lectern. That's why he's focusing on negative predicates, since the lectern he's talking about is necessarily itself, and it is a wooden lectern. And then the description is not picking out another lectern (another "name"), but the same one, even by the description.

That's why using "this" (though I'm picking up what you mean by "this" not being a name, now, ala Kripke -- since that's what he's speaking against, is Russel's theory of "this" counting as a name) with the lectern sunk home with me -- if descriptions are really all there are to names, then "this lectern is made of ice" is already picking out another lectern. That's why he's focusing on negative predicates, since the lectern he's talking about is necessarily itself, and it is a wooden lectern. And then the description is not picking out another lectern (another "name"), but the same one, even by the description — Moliere

"This lectern" is quite likely to be used as a rigid designator. Banno was throwing some spin in there. There might be cases where "this lectern" is non-rigid, but you'd have to pick that up from context.

Keep in mind that Kripke is focusing on ordinary language use. This is not an examination of a logical language, so meaning is truly use here.

In a case where "this lectern" is a rigid designator, the baptism is likely to have just happened. It's as if I named the lectern "Bob" but Bob equals this lectern.

The wooden lectern example is pointing to the way we think about objects. Note Kripke's emphasis on what we can and can't imagine. What he's saying should be very intuitive to you.

Keep in mind that Kripke is focusing on ordinary language use. This is not an examination of a logical language, so meaning is truly use here.

In a case where "this lectern" is a rigid designator, the baptism is likely to have just happened. It's as if I named the lectern "Bob" but Bob equals this lectern.

The wooden lectern example is pointing to the way we think about objects. Note Kripke's emphasis on what we can and can't imagine. What he's saying should be very intuitive to you. — frank

Heh, if so then I'm not understanding it because it is not very intuitive to me. :D

The bits on what we can and cannot imagine are somewhat opaque to me. Not that imagination isn't involved in thinking philosophically, but I'm naturally hesitant to say that imagination is the limit of philosophical thinking.

"This lectern" functions rigidly in the paper, I agree. It picks out the same object across possible-worlds/plausible-circumstances. I can see how that's not a name, but I don't think it matters either too much to this part of the argument if I'm reading it right at least.

Reading over it again now... I think the lectern example is where Kripke is showing how we can derive an a posteriori necessity.

So we have

P -> [] P

From a priori analysis of the lectern we can conclude that insofar that any particular lectern is made of wood, then it necessarily is not made of ice.

Then, from a posteriori investigation, we infer

P

That is, though we could be wrong, the lectern is made of wood.

Therefore, it is necessarily not made of ice

So we get a necessary conclusion from a proposition believed due to a posteriori methods.

So he's talking about, I gather, the distinction he wants to make between a posteriori/a priori, and contingent/necessary -- so that we can have necessary, a posteriori truths. (at least, as you note, within the way we normally use language rather than in some purified logical form)

My new understanding is: — RussellA

Cool.

You might find something interesting in the SEP article Reference. It lists four intertwined theories of reference:
1. Descriptions
2. Causal
3. Character
4. Intentionalist
My view is pretty noncommittal. Why not just accept that we can make reference to something in virtue of a range of different ways of using words, and hence that these are ways we use words to refer, but no one of them, and even no particular combination, is the way we refer.

But then sometimes I agree with Quine that reference is inscrutable.

What is difficult to maintain, after understanding Kripke's arguments, is that objects are constituted by essential properties.

The bits on what we can and cannot imagine are somewhat opaque to me. Not that imagination isn't involved in thinking philosophically, but I'm naturally hesitant to say that imagination is the limit of philosophical thinking. — Moliere

There's a long tradition of examining the ways we're bound to think. I think all philosophers make some use of that kind of exploration, but Hume and Kant are particularly notable for asking about the things we can and can't imagine. Kripke joins them in this for the purpose of showing that if we insist that all necessarily true statements are known a priori, this conflicts with the way we think about counterfactuals.

So there's no recipe here for speaking in a certain way. We're not identifying elements of grammar. We're analyzing a historic philosophical bias with the scalpel of...

the way we think. :grin:

So we get a necessary conclusion from a proposition believed due to a posteriori methods. — Moliere

Yep. We find necessarily true statements that are known a posteriori.

"This lectern" is quite likely to be used as a rigid designator. Banno was throwing some spin in there. There might be cases where "this lectern" is non-rigid, but you'd have to pick that up from context. — frank

Perhaps; and example would be useful. I can't think of one, although perhaps something along the lines of Donellan's man with a martini would work.

But it also seems to me that "Bob the lectern", "That lectern", and "The wooden lectern at the front of the room with 'Bob' engraved on it" - a proper name, a demonstrative and a definite description - might each pick out the lectern in different ways, requiring differing theories of reference.

Damn. Seems about right.

Counterfactual situations show that names do not refer in virtue of the properties or the descriptions of some object or individual.

And we must make a distinction between empirical, a posteriori stuff and grammatical, a priori stuff on the one hand, and necessary and contingent stuff, on the other.

hence,

We find necessarily true statements that are known a posteriori. — frank

But I wonder what you make of the last arguments of the article, concerning the sensation of heat and states of mind. I've suggested that this is a misapplication of Kripke's argument, since that argument relies on fairly clear individuation - objects and individuals; but that after Wittgenstein it's not so clear that sensations and states of mind are the requisite sorts of individuals.

Further, the sensation of cold does not correspond to temperature, as shown in the video, and particular brain states do not correspond to particular states of mind, as shown by the irregularity of neural networks.

There's much plumbing to be sorted here, it seems.

But I wonder what you make of the last arguments of the article, concerning the sensation of heat and states of mind — Banno

Honestly I have to rethink it now. I'm not sure anymore.

There's a long tradition of examining the ways we're bound to think. I think all philosophers make some use of that kind of exploration, but Hume and Kant are particularly notable for asking about the things we can and can't imagine. Kripke joins them in this for the purpose of showing that if we insist that all necessarily true statements are known a priori, this conflicts with the way we think about counterfactuals.

So there's no recipe here for speaking in a certain way. We're not identifying elements of grammar. We're analyzing a historic philosophical bias with the scalpel of...

the way we think. :grin: — frank

Okiedokie, if we're talking Hume/Kant then I'm on familiar ground.

So, compactly maybe: the historical philosophical use of imagination as a sort of ground for thinking about ordinary language's treatment of counter-factuals and contrasting that with the philosophic bias that all necessary and true statements are necessarily also known a priori.

So we can imagine this lectern is made of metal or in the next room, but we cannot imagine that this lectern was made from ice from the Thames. That's not plausible.

So, also, it seems that to make sense of this we have to accept Kripke's notion of "possible worlds" too. That, at least ordinarily, we can and do speak of possible worlds that pick out the same objects as the actual world, and so while this is a loose sense of "necessity" it's also one that people use.

Anyway, if we were to continue with the theme of reference, we might go to one of Donellan's papers, for more about why descriptions are not how reference works, or alternatively to Davidson's Reality without reference, a paper which had a thread here years ago.

Thoughts?

I wasn't able to find a copy of Davidson's paper that is not at least partially protected.

One of the things about the thermometer definition is it explicitly states how to pick out temperature without telling you anything about temperature. I think that's a feature. However, if we're talking in terms of ordinary usage, mine is definitely a specialized definition meant for scientific purposes of theorizing about temperature and heat, or really more specifically, meant to allow people to work together to create knowledge which utilizes those notions which come from that basic theorizing. It's not the ordinary sort of thing that we mean by "Bob" or "that" or, as it's purposefully trying to leave out a description so that multiple descriptions can work, certainly not a definite description. Neither is it quite a pronoun, or even a generic noun like "table", which picks out objects (where heat is harder to think of as an object, except in the logical sense, but that's already set to the side because we're talking about ordinary names)

I don't want to say that it's specialized, because I really doubt that, I'm just noting that I think it's still worth looking at those examples with some suspicion, upon thinking it through.

In the case of counter-factuals, when we're talking about "heat is the motion of molecules" vs. "heat is a caloric substance that goes from one object to the other", then I think both must be picking out the same things in the case of the first part, but I'm not sure about the latter part still. Unless I allow strange things like "the belief that "the motion of molecules" means any physical object that cannot be perceived by our bodily senses because of how small it is which is in fact moving somehow" to be picking out objects between participants in a conversation. Maybe! But it's worth noting that we're getting into strange territory here.

So I agree with your conclusion here for sure:

I've suggested that this is a misapplication of Kripke's argument, since that argument relies on fairly clear individuation - objects and individuals; but that after Wittgenstein it's not so clear that sensations and states of mind are the requisite sorts of individuals.

Further, the sensation of cold does not correspond to temperature, as shown in the video, and particular brain states do not correspond to particular states of mind, as shown by the irregularity of neural networks.

There's much plumbing to be sorted here, it seems. — Banno

I think that in his audience those examples were good to bring up because of the popularity, but that they are confusing to me, at least, for all the reasons we've already talked about and that you mention here.

Yep.

What is difficult to maintain, after understanding Kripke's arguments, is that objects are constituted by essential properties. — Banno

We can do this simply with the law of identity. It implies that each object is unique, whereas essential properties are what things of the same type have in common. Therefore an object must consist of more than just essential properties, by the law of identity. In Aristotelian terms, an object has accidendal properties as well as essential properties.

The problem is that the law of identity is just an assumption based in intuition, it really cannot be proven. Some might say it's self-evident, some might say it's a priori, but these things really don't stand to be proven. That's why some philosophers (like Hegel) will dismiss the law of identity. So Kripke seems to want to prove something like the law of identity. But he uses faulty premises and his argument is unsound, so he does nothing toward helping us to understand the issues, he only obfuscates them behind a cloud of confusion.

It's most likely the case that what Kripke is trying to prove really cannot be proven, so the only way for his argument to be successful is if he can use enough smoke and mirrors to hide the faults in his premises.

However, there is much more at stake here than what meets the eye. There is the issue of the difference between an actual object (supposed to have independent existence in the world), and a possible object, (one signified with a name or description, but not necessarily assumed to have independent existence). Kripke's mode of argument effectively dissolves this difference, and this I believe is a serious ontological problem.

Using Kripkean principles, how are we to distinguish between a named or described object which may or may not exist in the physical world, and a named or described object which is supposed to have real existence in the physical world? This is why I stated that if we do not accept that the real object is the Platonic idea, we are forced into anti-realism because there is no other option for a real object.

The problem is that the law of identity is just an assumption based in intuition, it really cannot be proven. — Metaphysician Undercover

Well maybe we can focus on this for a bit, at the risk of being off-topic.

The law of identity, like any law of logic, is a way of talking.

Asking for a proof of A=A is very much like asking for a proof that the bishop always moved diagonally. If it didn't move diagonally, it would not be the bishop. If A=A were wrong we would not be talking about A or =.

So it's not an intuition or an assumption.

Hence, it is not that "Kripke seems to want to prove something like the law of identity".

I think he takes it as given.

I think you misinterpret the law of identity. It says something about things, not something about the way we talk. It says that a thing is the same as itself. So if it says something about the way we talk, it is prescriptive, saying something about how we should talk. It is saying that we ought to talk about things as if they are the same as themselves. To use your bishop analogy, it's like whoever made up the game, making up the rules, saying we ought to have a piece which only moves diagonally, and this we will be called the bishop.

The law of identity is widely accepted, and that is because it is very intuitive. Logically though, we can deny it like Hegel does. We can argue for example, that in the act of becoming, which is the transition between not being and being what a thing is, the thing must exist as something because it's not not being, but it is also not the thing which it is when it is the thing which it is (by the law of identity). Hence the thing must be something, but something other than the thing which it is, in this mode of becoming.

So when we give priority to "becoming" as Hegel does in his dialectics, we can override the law of identity, asserting that the thing is something in this prior state, when it is becoming the thing that it will be, but is not yet that thing, and by Aristotelian principles it is only the potential to be that thing, which it will be by the law of identity. Then we say that the potential to be something is something. But since potential consists of many different possibilities, then the thing which that potential is, is like many different things at the same time. This violates the law of identity yet it is also very intuitive, if we allow that the possible thing is in some way a thing, because possibility is the potential for many different things. So we must violate that law when we say that the possibility for a thing is a thing.

Hence, it is not that "Kripke seems to want to prove something like the law of identity".

I think he takes it as given. — Banno

I find it quite clear that he does not take it as a given. From what he writes, he obviously knows the law, and its meaning. But then he questions it, and so he has to find a way to state it which suits his purpose, 'If the table is not made of ice it is necessarily not made of ice' for example. This is just a reformulation of the law, a thing is necessarily the thing which it is. But he has qualified it with the empirical judgement of what the thing is, a wooden table, and restates it as a conditional. Notice he could state the conditional any way "if it's made of wood..." "if its made of rock..." etc.. So what he states has been derived from the law of identity but is a completely different form, being expressed as a specific conditional, rather than the general law.

Furthermore his "rigid designators" demonstrate that he actually has no respect for the law of identity at all. In each possible world, the thing denoted by the rigid designator is different from what it is in other possible worlds, having different properties. Yet he says that these different things are the same thing. Therefore "a thing is the same as itself" is very clearly violated.

One of the things about the thermometer definition is it explicitly states how to pick out temperature without telling you anything about temperature. I think that's a feature..........In the case of counter-factuals, when we're talking about "heat is the motion of molecules" vs. "heat is a caloric substance that goes from one object to the other", then I think both must be picking out the same things in the case of the first part, but I'm not sure about the latter part still. — Moliere

The example of the thermometer may be a key into Kripke's necessary a posteriori.

We may know an effect without needing to know its cause
I observe the number on a thermometer change. I don't know what is causing the number to change, but I name whatever is causing the number to change as heat. The number isn't heat, but what is causing the number to change is heat.

Some hypothesise that what is causing the number to change is the motion of molecules, ie, heat is the motion of molecules. Others hypothesise that what is causing the number to change is caloric, ie, heat is caloric. If one of these hypothesise becomes with time self-evidently true, it becomes an axiom. Society then accepts as given the axiom that heat is the motion of molecules.

Both the motion of molecules and caloric are referring to the same thing, heat in the world, even if we never actually know what heat in the world is. In practice, we don't need to know what is causing the numbers to change, we don't need to know what heat in the world is, all we need to know is the effect of heat in the world, the numbers changing on the thermometer.

As long as we know the effect of heat, we don't need to know what heat is.

Kripke is using the word "heat" in two very different ways
We can have a particular sensation, which we name the sensation of heat. We name the cause of this particular sensation heat. The word heat is being used in two different ways, one as a name of an effect, the sensation of heat, and the other as the name of its cause, heat. The effect is very different from the cause, though they share the same name.

Kripke refers to the sensation of heat. Page 185: "There is a certain external phenomenon which we can sense by the sense of touch, and it produces a sensation which we call “the sensation of heat.”"

Kripke also refers to heat as the motion of molecules. Page 170: “Heat is the motion of molecules.”

Heat as the sensation of heat in the mind
Kripke discusses possible connections between the sensation of heat and its cause: i) "So, it might be thought, to imagine a situation in which heat would not have been the motion of molecules" ii) "the motion of molecules but in which such motion does not give us the sensation of heat" iii) "Martians, who do indeed get the very sensation that we call “the sensation of heat” when they feel some ice which has slow molecular motion, and who do not get a sensation of heat—in fact, maybe just the reverse".

Heat as the cause in the world of the sensation of heat in the mind
Kripke discusses possible causes of our sensation of heat: i) "First, imagine it inhabited by no creatures at all: then there is no one to feel any sensations of heat" ii) "the judgment that heat is the motion of molecules would have been false."

Rigid designators
The motion of molecules in the world is a rigid designator. As this lectern is made of wood , this lectern is necessarily made of wood, similarly, as these molecules are in motion they are necessarily in motion.

A sensation of heat in the mind is a rigid designator. As this particular sensation of heat in the mind is this particular sensation, it is necessarily this particular sensation, whatever it is named, in that it could have been named "heat", "cold", "apple" or "The Eiffel Tower".

Heat in the world as the cause of a sensation of heat in the mind is a rigid designator. As this lectern is made of wood , this lectern is necessarily made of wood, similarly heat in the world as the cause of a sensation of heat in the mind is necessarily the cause of the sensation of heat in the mind, whatever it is named.

Kripke concludes that heat is necessarily the motion of molecules
He wrote: page 187: "To state the view succinctly: we use both the terms ‘heat’ and ‘the motion of molecules’ as rigid designators for a certain external phenomenon. Since heat is in fact the motion of molecules, and the designators are rigid, by the argument I have given here, it is going to be necessary that heat is the motion of molecules."

There are two possible meanings to heat is necessarily the motion of molecules
The motion of molecules in the world has one possible meaning, although heat has two possible meanings.

Meaning one: Heat in the world is necessarily the motion of molecules in the world. There may be heat in the world, and there may be molecules in motion in the world. Both the heat in the world and molecules in motion in the world are rigid designators, but it doesn't of necessity follow that there is a link between them. For example, both "Nixon" and "Caesar" are rigid designators in all possible worlds, but there is no necessary link between them.

Meaning two: Heat in the mind is necessarily the motion of molecules in the world. The sensation of heat in the mind is necessarily caused by heat in the world, but as there is no necessary link between heat in the world and the motion of molecules in the world, there is no necessary link between the sensation of heat in the mind and the motion of molecules in the world.

Conclusion
Heat is not necessarily the motion of molecules.

Temperature is a measure of the average kinetic energy of the molecules of a substance.

In chemistry and physics, heat is the quantity of energy available for transfer between a system and its surroundings.

See the second video given previously. The sensation of heat is related to temperature, but more to the the rate of transfer of energy.

The amount of heat gained or lost by a sample (q) can be calculated using the equation q = mcΔT, where m is the mass of the sample, c is the specific heat, and ΔT is the temperature change. — Khan

Heat is necessarily the motion of molecules.

The sensation of heat is not.

Again, Kripke's choice of example was poor. But this does not undermine the broader case that sometimes if A=A, then ☐A=A.

But it must be kept in mind that this is a way to choose what counts as A

However, there is much more at stake here than what meets the eye. There is the issue of the difference between an actual object (supposed to have independent existence in the world), and a possible object, (one signified with a name or description, but not necessarily assumed to have independent existence). — Metaphysician Undercover

Here again is the issue of transworld identity. Kripke's answer is now the standard response.

I might have put my slippers on. I didn't. One way to express this is that in some possible world I put my slippers on. It is trivial that the person who, in that possible world, put on their slippers, was me. There is no issue of "the difference between an actual object and a possible object.

Kripke's mode of argument effectively dissolves this difference, and this I believe is a serious ontological problem. — Metaphysician Undercover

Yep.

There is more.

The most influential arguments against the view that there is a genuine problem of transworld identity (or ‘problem of transworld identification’, to use Kripke’s preferred terminology) are probably those presented by Plantinga (1973, 1974) and Kripke (1980). Plantinga and Kripke appear to have, as their target, an alleged problem of transworld identity that rests on one of three assumptions. The first assumption is that we must possess criteria of transworld identity in order to ascertain, on the basis of their properties in other possible worlds, the identities of (perhaps radically disguised) individuals in those worlds. The second assumption is that we must possess criteria of transworld identity if our references to individuals in other possible worlds are not to miss their mark. The third assumption is that we must possess criteria of transworld identity in order to understand transworld identity claims. Anyone who makes one of these assumptions is likely to think that there is a problem of transworld identity—a problem concerning our entitlement to make claims that imply that an individual exists in more than one possible world. For it does not seem that we possess criteria of transworld identity that could fulfil any of these three roles. However, Plantinga and Kripke provide reasons for thinking that none of these three assumptions survives scrutiny. If so, and if these assumptions exhaust the grounds for supposing that there is a problem of transworld identity, the alleged problem may be dismissed as a pseudo-problem. — SEP

One way to argue in favour of transworld identity (distinct from the defensive strategies discussed in Sections 4 and 5 above) is what we might call ‘the argument from logical simplicity’ (Linsky and Zalta 1994, 1996; Williamson 1998, 2000). The argument begins by noting that Quantified Modal Logic—which combines individual quantifiers and modal operators—is greatly simplified when one accepts the validity of the Barcan scheme, ∀x□A → □∀xA (Marcus 1946). The resulting logic is sound and complete with respect to constant domain semantics, in which each possible world has precisely the same set of individuals in its domain. The simplest philosophical interpretation of this semantics is that one and the same individual exists at every possible world. — SEP

To be sure, there are issues with transworld identity. They are not the issues Meta cites.

This will not answer the question for Meta. But keep in mind that Meta thinks $0.\dot 9 \neq1$

I think you misinterpret the law of identity. — Metaphysician Undercover

Fair enough. I don't think it's me.

In several posts you mistook other theorems for A=A. So take

'If the table is not made of ice it is necessarily not made of ice' for example. This is just a reformulation of the law, — Metaphysician Undercover

But P⊃☐P is invalid, and hence it cannot be an"reformulation" of P=P. And Kripke very carefully does not treat it as such. No consistent substitution into P=P will give P⊃☐P.

In each possible world, the thing denoted by the rigid designator is different from what it is in other possible worlds, having different properties. — Metaphysician Undercover

This shows that your misunderstanding stems from the error I pointed out in my previous reply to you. The very same thing may have different properties in each possible world under consideration. It is the error Kripke describes here:

among the defenders of quantified modal logic and among its detractors. All of this talk seems to me to have taken the metaphor of possible worlds much too seriously in some way. It is as if a 'possible world' were like a foreign country, or distant planet way out there. It is as fi we see dimly through a telescope various actors on this distant planet. — p.174

Here again is the issue of transworld identity. Kripke's answer is now the standard response. — Banno

But the issue is not whether it is the "standard" response, the point is that it is not consistent with the law of identity, not whether or not it is the standard. As you may have noticed, I argue against standard mathematical axioms as violating the law of identity. That law was introduced by Aristotle to rid us of the sophistry produced by Platonic "objects". It effectively eliminates human ideas and formulae from having an identity as an object, by stipulating that identity is something unique to the particular, or individual.

There is no immediate problem in violating or denying the law of identity, as I explained in the last post. When we place "becoming", (the potential to be an object), as prior to actually being an object, and we give identity to that possibility of an object, instead of assigning identity to the actual material object, we circumvent the law of identity. But when this happens we are vulnerable to the type of sophistry which Aristotle formulated the law of identity to combat.

I might have put my slippers on. I didn't. One way to express this is that in some possible world I put my slippers on. It is trivial that the person who, in that possible world, put on their slippers, was me. There is no issue of "the difference between an actual object and a possible object. — Banno

If you call violating the law of identity "trivial" then it is trivial. In your example, the fact is that you did not put your slippers on. If you conceive of a counterfactual in which you did put your slippers on, then the person in that possible world is not you, because you put your slippers on. It's just an imaginary Banno, the real Banno did not put slippers on. No stretch of the imagination will provide equivalence between these two. In one case we have a real existing person without slippers and in the other there is a fictional person with slippers. It's not you. That's plain, simple, and obvious. And, if we insist that the two are both the same person we violate the law of non-contradiction because we have the very same person with two contradicting properties (slippers on and slippers off) at the same time.

If instead, I didn't know whether you put your slippers on or not, and I want to consider both as real possibilities, then the issue is more difficult. I want to say that in one possible world Banno put his slippers on, and in another possible world Banno did not put his slippers on. I have no empirical observations of the real Banno, but I believe there is one, so I want to allow that this real person identified as "Banno", is represented in each of these logical possibilities. But really, these are only 'possible Bannos', one with slippers on, the other without. The real individual represented by "Banno" is somewhere else, and I only have fictional, possible Bannos. And this is where the matter gets tricky, because by the law of identity we must conclude that the real object identified as Banno is separate, distinct from these 'possible Bannos'. The 'possible Bannos' simply have no real identity. And trying to produce an identity for them will be an endless nightmare.

I think it is important to maintain this separation if we want to maintain a realist ontology. I want to say that independent of the two 'possible Bannos' there is a separate 'actual Banno', and the correct possible Banno is the one that corresponds with the actual Banno. So I say that the name "Banno" signifies a real object, the actual Banno, and in the possible worlds this name "Banno" holds a place for a possible representation of the actual Banno.

If we do not maintain this principle, that the name refers to an actual Banno, independent of the possibilities, then we allow for different sorts of non-realist ontology. Then there is no separate, actual object, only the supposed 'possible objects', and the correct possibility is decided by means other than correspondence with the real world, like in model-dependent realism.

In several posts you mistook other theorems for A=A. — Banno

Do you recognize that "A=A" is a symbolic representation of the law of identity, which is properly stated as an object is the same as itself?

But P⊃☐P is invalid, and hence it cannot be an"reformulation" of P=P. And Kripke very carefully does not treat it as such. No consistent substitution into P=P will give P⊃☐P. — Banno

I told you, the law of identity is not supposed to be valid, it is meant as a simple axiom, a self-evident truth. There is no validity to it, it is simply intuitive. So that "P⊃☐P is invalid" says nothing about whether it is a formulation of the law of identity or not.

So take the example, "if the table is not made of ice it is necessarily not made of ice". How do you validate "necessarily" here, without reference to the law of identity? You yourself say that this statement is not valid. However, the law of identity may be seen to support the use of "necessarily" here. The law of identity is a statement of necessity, an object is necessarily the same as itself. That's the way Aristotle described this law in his Metaphysics, for the very reasons explained above. When an object comes into being it is necessarily the object which it is, and not something else. That's a statement based in the nature of time, what has come to be is necessarily so. Banno is necessarily the individual who did not put his slippers on. The table is necessarily the table which it is. If it is made of wood, and not made of ice, then it is necessarily made of wood and not made of ice. The use of "necessarily" is supported by the law of identity. What has come to be is necessarily so. An object is necessarily the object which it is, i.e. the same as itself. The object which we call "the table" is necessarily the object which it is, i.e. the same as itself, therefore if it's not made of ice it is necessarily not made of ice.

The very same thing may have different properties in each possible world under consideration. — Banno

That is very clearly a violation of the law of identity. In a possible world there is only possible things. So there are no things with an identity in a possible world. "The very same thing" can only refer to an actual thing. If we allow that the very same thing has different (contradicting) properties at the same time, in different possible worlds, then the law of non-contradiction is violated. The claim of "different possible worlds" does not provide an exception to the rule, because it is asserted that it is the very same thing, and clearly it cannot be the very same thing with contradicting properties at the same time. You might say it's a possible thing in a possible world, but then it has no identity and cannot be said to be the very same thing. Therefore we must adhere to the law of identity to avoid this contradiction, and maintain that there is only possibilities in possible worlds. And possible worlds are imaginary, so there are no things with an identity of their own in these statements of possibility. We ought to avoid that nightmare and quit looking for such an identity

If you conceive of a counterfactual in which you did put your slippers on, then the person in that possible world is not you, because you put your slippers on. — Metaphysician Undercover

Yeah, it is me. That's implicit in "I might have put my slippers on". It's a sentence about me, not about someone else.

And from there, your account goes astray. What follows in your post is erroneous.

Yeah, it is me. That's implicit in "I might have put my slippers on". It's a sentence about me, not about someone else. — Banno

But it's false, you did not put your slippers on. When you say "I might have put my slippers on" you are lying because you know that you did not. Therefore the statement doesn't serve to identify you, it can only mislead if we think that it does. That's where the problem lies. We ought not think that falsities serve to identify. The person identified in that statement as "I" is not a real person, because the statement is false, and the person stating it is not truthful because the real person did not put slippers on, and knows this.

And from there, your account goes astray. What follows in your post is erroneous. — Banno

This only follows if what you say is the truth. But it's not. You lie when you say ""I might have put my slippers on" when you know that you did not put your slippers on. Therefore the "I" does not refer to you personally, it refers to a deceptive image of you, a fiction. And no matter how you insist that it does refer to you, you are lying and it's all a deception.

So be it, if your will is to insist on deceiving.

if we insist that the two are both the same person we violate the law of non-contradiction because we have the very same person with two contradicting properties (slippers on and slippers off) at the same time. — Metaphysician Undercover

The possible world in which I have slippers on is not the one in which I have slippers off. Whether you like it or not, this is not a contradiction. The modal logic is consistent, as Kripke and others have shown in their considerations of possible world semantics.

Do you recognize that "A=A" is a symbolic representation of the law of identity, which is properly stated as an object is the same as itself? — Metaphysician Undercover

That's what I am saying. Yep. But without the metaphysical baggage you attach. A=A is valid. It is a necessary truth. When you say stuff like

the law of identity is not supposed to be valid — Metaphysician Undercover

one is left to puzzle over the logic you are using.

How do you validate "necessarily" here, without reference to the law of identity? — Metaphysician Undercover

Simply, a sentence will be necessarily true only if it is true in every possible world.

Banno is necessarily the individual who did not put his slippers on. — Metaphysician Undercover

No, I'm not. It is not true that I did not put on my slippers in every possible world, because having my slippers on is not a necessary attribute of Banno.

In a possible world there is only possible things. — Metaphysician Undercover

Again, no, since the actual world is a possible world. That's been explained to you before.

But it's false, you did not put your slippers on — Metaphysician Undercover

Sure, it's false in this possible world. You are left in the absurd position that the sentence "Banno might not put his slippers on" is not about me.

Anyway, I hope it is clear to others that Meta's account is quite at odds with Kripke's, and since there is little chance of Meta coming to understand modal logic, I'll finish up here; unless someone else has questions or comments regarding Meta's account.